You wish to save for your child's college education. Your goal is to have $$360,000$ when your child starts college at age $18.$ If you invest $$48,000$ when your child is born, what annual rate of interest must you earn to reach your goal?

Group of answer choices

$41\mathrm{.}67\%$

$11\mathrm{.}99\%$

$7\mathrm{.}50\%$

$11\mathrm{.}84\%$

$12\mathrm{.}25\%$

$20\mathrm{.}25\%$